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New and improved key-homomorphic pseudorandom functions. Cryptology ePrint Archive, Report 2014/074 (2014)
| Citations: | 8 - 3 self |
BibTeX
@MISC{Banerjee14newand,
author = {Abhishek Banerjee and Chris Peikert},
title = {New and improved key-homomorphic pseudorandom functions. Cryptology ePrint Archive, Report 2014/074},
year = {2014}
}
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Abstract
A key-homomorphic pseudorandom function (PRF) family {Fs: D → R} allows one to efficiently compute the value Fs+t(x) given Fs(x) and Ft(x). Such functions have many applications, such as dis-tributing the operation of a key-distribution center and updatable symmetric encryption. The only known construction of key-homomorphic PRFs without random oracles, due to Boneh et al. (CRYPTO 2013), is based on the learning with errors (LWE) problem and hence on worst-case lattice problems. However, the security proof relies on a very strong LWE assumption (i.e., very large approximation factors), and hence has quite inefficient parameter sizes and runtimes. In this work we give new constructions of key-homomorphic PRFs that are based on much weaker LWE assumptions, are much more efficient in time and space, and are still highly parallel. More specifically, we improve the LWE approximation factor from exponential in the input length to exponential in its logarithm (or less). For input length λ and 2λ security against known lattice algorithms, we improve the key size from λ3 to λ bits, the public parameters from λ6 to λ2 bits, and the runtime from λ7 to λω+1 bit operations (ignoring polylogarithmic factors in λ), where ω ∈ [2, 2.373] is the exponent of matrix multiplication. In addition, we give even more efficient ring-LWE-based constructions whose key sizes, public parameters, and incremental runtimes on consecutive inputs are all quasi-linear Õ(λ), which is optimal up to polylogarithmic factors. To our knowledge, these are the first low-depth PRFs (whether key homomorphic or not) enjoying any of these efficiency measures together with nontrivial proofs of 2λ security under any conventional assumption. 1
Keyphrases
key-homomorphic pseudorandom function cryptology eprint archive public parameter key-homomorphic prfs polylogarithmic factor input length key size consecutive input many application bit operation value f family f first low-depth prfs key-distribution center key homomorphic strong lwe assumption efficient ring-lwe-based construction lattice algorithm large approximation factor known construction matrix multiplication lwe assumption nontrivial proof inefficient parameter size incremental runtimes lwe approximation factor conventional assumption new construction random oracle updatable symmetric encryption worst-case lattice problem security proof relies
